<p><b>Abstract</b>—We study the parallel scheduling problem for a new modality of parallel computing: having one workstation "steal cycles" from another. We focus on a draconian mode of cycle-stealing, in which the owner of workstation <it>B</it> allows workstation <it>A</it> to take control of <it>B</it>'s processor whenever it is idle, with the promise of relinquishing control <it>immediately</it> upon demand. The typically high communication overhead for supplying workstation <it>B</it> with work and receiving its results militates in favor of supplying <it>B</it> with large amounts of work at a time; the risk of losing work in progress when the owner of <it>B</it> reclaims the workstation militates in favor of supplying <it>B</it> with a sequence of small packets of work. The challenge is to balance these two pressures in a way that maximizes the amount of work accomplished.</p><p>We formulate two models of cycle-stealing. The first attempts to maximize the expected work accomplished during a single episode, when one knows the probability distribution of the return of <it>B</it>'s owner. The second attempts to match the productivity of an omniscient cycle-stealer, when one knows how much work that stealer can accomplish. We derive optimal scheduling strategies for sample scenarios within each of these models.</p><p>Perhaps our most important discovery is the as-yet unexplained coincidence that two quite distinct scenarios lead to almost identical unique optimizing schedules. One scenario falls within our first model; it assumes that the probability of the return of <it>B</it>'s owner is uniform across the lifespan of the episode; the optimizing schedule maximizes the expected amount of work accomplished during the episode. The other scenario falls within our second model; it assumes that <it>B</it>'s owner will interrupt our cycle-stealing at most once during the lifespan of the opportunity; the optimizing schedule maximizes the amount of work that one is guaranteed to accomplish during the lifespan.</p>